Actually you are a good customer even if you pay it off in full. They way it works is as follows:

Merchant get charged from 1.15% to 4% on the transaction.

The merchant's bank pays Visa about 1.05% and keeps the rest above 1.05%

Visa then pays the your credit card company 1.00% on the transaction.

So even if you pay on time your bank gets 1% of the money you spend on the card. Visa only make about 0.05% of all money spent on visa BUT THIS IS MASSIVE.

Visa then pay the airline for the miles at say a discounted rate of about 0.6 cents per mile and make 0.4% for every dollar you spend. They then make the REAL profit on you paying interest.